No way, the communication protocol of DS and 3DS games is completely different
But since you will need CFW to use a TTDS, you will be able to install any 3DS game to the console's SD without any flashcard required (or you could buy an R4i Gold r4ids.cn and a way overpriced Sky3DS if you really didn't want to mod your console)

Yes if you're launching it through NTR Launcher (a DSiware homebrew); obviously you need to mod your consoles first

No way, the communication protocol of DS and 3DS games is completely different
But since you will need CFW to use a TTDS, you will be able to install any 3DS game to the console's SD without any flashcard required (or you could buy an R4i Gold r4ids.cn and a way overpriced Sky3DS if you really didn't want to mod your console)